The solution to the Tullock rent-seeking game when R>2: Mixed-strategy equilibria and mean dissipation rates

In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R>2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents.     

Endogenous sharing rules in collective-group rent-seeking

This paper examines the possibility of endogenous determination of intra-group sharing rules in a collective-group rent-seeking game. Collective-group rent-seeking is considered as a two-stage Nash-Cournot game in which sharing rules are determined prior to individual decision on voluntary contribution. The solution is subgame perfect and is obtained by backward induction. In competition between two groups of the same size, the Nash equilibrium sharing rule of each group is to distribute rent to each according to relative effort. Total rent-seeking outlays in this case are equal to those obtained by Tullock (1980). When more than two groups compete for a rent, the sharing rule based on relative effort is again likely to be the Nash equilibrium strategy of each group. The amount of total rent-seeking outlays is also equal to that in Tullock (1980). In a nutshell, the rent is substantially dissipated if sharing rules are endogenously determined.     

Tullock's rent-seeking contest with a minimum expenditure requirement

We consider a rent-seeking contest of the kind introduced by Tullock (1980) in which two players compete for a monopoly rent. We extend the contest by requiring that if a player puts forward an effort, his expenditures must be larger than or equal to some minimum level. We show that, depending on the model parameters, the number of Nash equilibria of the extended model can be zero, one, two or four. Furthermore, it turns out that the extent of rent dissipation in a Nash equilibrium of the extended model can be larger than, equal to, or smaller than the extent of rent dissipation in the unique Nash equilibrium of the original model.     

Rent-seeking with non-identical sharing rules

The primary object of this paper is to examine the role of differential sharing rules within a collective rent-seeking setting on the possible non-existence of Nash equilibrium. Focusing on groups that distribute part of the rent equally among their members and the residual according to relative effort, we show that in rent-seeking societies applying the two polar sharing rules equilibrium never exists. In the general case where groups apply different but not necessarily the polar sharing rules, we study the relationship between group variability in distributing rents and the problem of non-existence of equilibrium in the rent-seeking game.     

Asymmetric Rent-Seeking with More than Two Contestants

This article considers a rent-seeking model with N asymmetriccontestants. Each contestant may have a different valuation ofthe rent or a different relative ability to win the rent. Oneof the N contestants is selected as the winner based onTullock's probabilistic contest rule with constant returns toscale. A pure strategy Nash equilibrium solution is obtainedand its consequences are investigated.     

The uniqueness of pure-strategy Nash equilibrium in rent-seeking games with risk-averse players

This article proves that if each player’s measure of absolute risk aversion is nonincreasing in his/her wealth, then there exists a unique pure-strategy Nash equilibrium in the general rent-seeking game, where risk-averse players can coexist with risk-neutral players, attitude toward risk can differ among players, and concave production functions for lotteries are not necessarily the same among players.     

Do too many cooks always spoil the stew? An experimental analysis of rent-seeking and the role of a strategic buyer

Laboratory methods are used to evaluate the effects of institutional arrangements and rent-defending activity on rent-seeking auction outcomes. In part, Nash equilibrium predictions are a useful behavioral guide: As predicted, more rents are dissipated in perfectly-discriminating auctions, where the high-bidder wins, than in lotteries, where relative bids determine the chance of winning. Also as predicted, the introduction of a rent-defending buyer reduces social costs. Nevertheless, the social costs of rent-seeking consistently exceed predicted levels. Moreover, individual bidding, especially by buyers, deviates markedly from Nash predictions.     

Rent-seeking behaviour of retaliating agents

This paper has examined a rent-seeking game where the players take a more sophisticated approach to evaluating the potential strategies and counter-strategies of their rivals than in the standard Nash case. We have derived the conditions for the existence of symmetric and nonsymmetric equilibria for the game and derived the properties of these equilibria. Three results merit repeating. First, we find that rent dissipation will not, in general, be complete. Second, and in contrast to much of the traditional literature, we find that the socially optimal result of zero rent-seeking is sometimes a feasible equilibrium outcome for our game. Finally, there exist rent-seeking configurations in which the best play of one of the rivals is to withdraw from the game or, alternatively stated, where it is not optimal for a rival to contest the rent by entering the game. In these nonsymmetric cases it would appear that Tullock's conjecture about the value of preemptive moves remains valid. This is true even when the strategies and counter-strategies available to the players are much more complex than in the traditional Nash approach.As a final point we raise the issue of whether or not it is reasonable to suppose that the players in rent-seeking games will take their strategy and counter-strategy sets to be as large as we have assumed in this paper. Players may well make their moves and counter-moves based upon rules of thumb or other considerations that effectively bound the strategy sets of the players. As well, it may be useful to consider games where players, upon entering the game, commit themselves to a given level of expenditures. Many of these issues are considered in a related paper by the authors.     

Rent-seeking in natural resource quota allocations

This paper examines the incentives for rent-seeking in the allocation of natural resource quotas to competing user groups by political bodies. The political body has discretion in making the allocation, and competing user groups rent-seek to influence the allocation. We investigate ways in which the governmental body can affect the behavior of the players by setting the ground rules for the competition. A political body can affect an allocatively (Pareto) efficient outcome by choosing an appropriate default (pre rent-seeking) policy. Surprisingly, an allocatively efficient default policy is unlikely to minimize social costs. However, winner-take-all default policies are likely to maximize, not minimize, rent-seeking. A competitive post-allocation market reduces rent-seeking, but is not, either itself or in combination with an efficient default policy, capable of minimizing social costs. However, forcing winners in political redistributions to fully compensate losers both lowers the rent-seeking levels relative to a potential compensation criterion and, when used together with an efficient default policy, is capable of obtaining the first-best solution of an allocatively efficient allocation with zero rent-seeking.     

Rent-seeking and optimal regulation in replenishable resource industries

In this paper, wasteful rent-seeking behaviour has been shown to have important implications for the determination of the welfare maximizing regulatory policies of replenishable natural resource industries. In general, the incorporation of wasteful rent-seeking activity into the analysis leads to policies which suggest a greater level of industry output than has been advocated by tradition policies that do not take rent-seeking into account. Our analysis therefore supports a more laissez faire policy than has been recommended in the literature.Specifically, we find that when rents are completely dissipated by wasteful rent-seeking activity (t = 1), the role of the regulator is simply to guarantee biological efficiency, should this be threatened by the economic equilibrium achieved by the free-access of firms. One of two possibilities can occur. In the first, the economic equilibrium determined by the free-access of firms is biologically efficient, i.e., the equilibrium steady state of the replenishable natural resource exceeds or is equal to the maximum sustainable yield stock size (x _MSY). If this occurs, the regulator needs to take no action whatsoever. In the second case, the economic equilibrium generated by the free-access of firms does not yield biological efficiency. The equilibrium is characterized by a steady state stock of the natural resource that is smaller that the maximum sustainable yield stock size, namely (x _MSY <>x _MSY). In this case, therefore, the regulator does need to intervene, but his best policy takes the simple form of setting the total quota equal to the maximum sustainable yield (MSY) of the resource. Thus, while the results are to some extent consistent to those derived by Buchanan for the regulation of externalities, the fact that we are dealing here with replenishable resources adds a further dimension to the issue and changes some of the policy implications.     

Third parties in equilibrium: comment and correction

Published in a past issue of this journal, Hug (Public Choice 82:159–180, 1995) studies political competition among three vote-maximizing parties when voters cannot know exactly which policies the parties will adopt when elected. Contrary to what is claimed in Proposition 3, in the generic case the game has no Nash equilibrium in pure strategies. In this case, only a local Nash equilibrium (LNE) may exist, but due to an incorrect second order condition, the conditions in Proposition 3 do not characterize this LNE either.     

Rent-seeking and the two-track price system in China

A simple general equilibrium model is specified to analyse the impact on the Chinese economy of the introduction of a two-track price system on to a centrally-planned economy. It is shown that national income will rise as a result together with a fall in the costs associated with rent-seeking. Some estimates of welfare gains and costs of rent-seeking are provided for seven commodities within a partial equilibrium framework. They are shown to be dependent on the price elasticities of demand and supply. The latter determine the ratio of plan to market prices and the share of plan in total output.     

Rent-seeking with asymmetric valuations

This paper analyzes Tullock's rent-seeking game with asymmetric valuations for a variable range of the returns to scale parameter. A necessary and sufficient condition for a unique pure strategy Nash equilibrium is established. Equilibrium effort and expected profits are determined and subjected to comparative statics analysis. Increasing the underdog's valuation induces both players to increase their efforts. Increasing the favorite's valuation increases his effort but decreases the effort of the underdog. Expected profits increase with a player's valuation but decreases with the valuation of the competitor. The impact of the returns to scale parameter is also analyzed.     

Risk aversion in two-period rent-seeking games

This work analyzes a two-period rent-seeking game, with the aim of studying the effect of risk aversion on the optimal choices made by the rent-seekers. We first prove that the equilibrium in two-period rent-seeking games always is unique. The analysis also shows that more risk aversion reduces the investment in the rent-seeking game in a two-period framework without introducing the additional condition of prudence, required in one-period models. Similarly, the introduction of a risky rent, instead of a given rent, implies, in the two-period framework, a reduction in investment under the condition that the rent-seekers are risk averse. Moreover, with risk aversion, larger first-period wealth increases investment in the rent-seeking game and larger second-period wealth reduces it. When both first-period and second-period wealth increase, investment in the rent-seeking game declines if the rent-seeker is risk averse and imprudent. Lastly, when a risky level of second-period wealth is introduced, the rent-seeker increases (reduces) investment in the rent-seeking game if he is risk averse and prudent (imprudent).

     

Rent-seeking with non-identical sharing rules: An equilibrium rescued

Nitzan's (1991) analysis of differential sharing rules in a collective rent-seeking setting is reconsidered. Two groups, each with more than one member, are presumed to use different linear combinations of two sharing rules, one based on an equal-division of the prize, and the other on each member's relative effort. We show that an equilibrium always exists for this type of game, and then characterize the equilibrium. Our result is contrary to Nitzan's claims that (a) in the general case an equilibrium often does not exist, and (b) an equilibrium never exists when the groups use the polar extreme rules.     

How organizational structure can reduce rent-seeking

In multi-tiered organizations, individuals can engage in unproductive rent-seeking activities both within and between the divisions of the organization. Nevertheless, a multi-tiered organizational structure can induce efficiency gains by decreasing rent-seeking. We present a model of production and simultaneous internal and external rent-seeking, assuming a logistic contest success function. In equilibrium, there is generically either internal or external rent-seeking, but not both. A multi-tiered organization leads to less rent-seeking and higher welfare, even though the production technology gives no reason for any specific organizational structure. Our findings constitute a new efficiency rationale for multi-tiered organizations.     

Three-candidate spatial competition when candidates have valence: stochastic voting

We study the effects of stochastic (probabilistic) voting on equilibrium locations, equilibrium vote shares and comparative statics in a setup with three heterogeneous candidates and a single-dimensional issue space. Comparing the equilibria with and without stochastic voting, we find that under an appropriate level of uncertainty about voter behavior, the model has a pure strategy Nash Equilibrium (PSNE) that is free from several non-plausible features of the PSNE under deterministic voting. This result is robust to extensions to asymmetric density and plurality maximization.     

Some Implications of Corporate Taxation for Rent-Seeking Activity

In this paper we show that corporate taxes are likely to have considerable implications for rent-seeking activity. We find that corporate taxation tends to significantly reduce rent-seeking, and that it favors rent-seeking by established firms and discriminates against new and zero profit firms. Indeed, we show that corporate tax regulations may completely block rent-seeking by new corporations, and that rent-seeking competitions may be characterized by an equilibrium that features a small number of profitable and well established firms. Tax regulations may therefore impart an oligopolistic tendency to rent-seeking markets. Moreover, our results may have significant implications for the effects of corporate taxes on patent races, tournaments, and other first-past-the-post competitions.     

Delegation with multiple instruments in a rent-seeking contest

We consider delegation in a rent-seeking contest with two players, where delegates have more instruments at their disposal than the main players. We endogenize both the decision to hire a delegate and the contingent fee offered to the delegates. We characterize the situations when either no, one or two players hire a delegate in equilibrium. We show that the decision to hire a delegate depends in a non-monotonic way on the size of the contested prize.     

Rent seeking and rent setting with asymmetric effectiveness of lobbying

This paper provides a more general model of the determination of rent-seeking costs by combining the following features: endogenous rent determination, asymmetric effectiveness of contending agents in their lobbying efforts, and multiple periods. In doing so, the paper generalizes some aspects of the work of Applelbaum and Katz (1987), Rogerson (1982), Leininger (1992) and Kohli (1992). Some results obtained are: (i) in the short run, when the regulator's salary is higher than in an alternative occupation, both the per unit cost of rent-seeking and the total rent set by regulator are highest for the same value of the relative effectiveness parameter; (ii) in the long run, an increase in the effectiveness parameter leads to a reduction in the social costs of rent seeking; (iii) in a repeated game, the equilibrium rent is lower the higher is the regulator's discount factor.